In a stand mixer. beat butter and sugar until light. Add eggs one at a time. Add vanilla. In a separate bowl, add all dry ingredients and mix well. Remove bowl from mixer and with a spoon, add 1/2 of the flour mixture. Stir in milk and then add remaining flour mixture. Combine well.
Turn dough out onto a floured board and form it into a ball. Halve it and form each half into a log approximately 12 inches long and 2 inches wide. Arrange logs on a buttered and floured baking sheet about 3 inches apart.
Bake logs in the middle of the oven for 40 minutes or until they are firm all over and browned. Remove them from the oven, let cool a few minutes. On a cutting board, slice logs on a diagonal about 1/2 inch thick. Arrange slices back on baking sheet and bake them approximately 10 minutes on each side or until golden throughout. Cool biscotti to room temperature. Store in airtight containers in single layers between waxed paper for up to 2 weeks.